-0-23 x-5 cosec x- x-cosec x d x-

The correct option is D 2 π∫_0^π/2 3 sec x+5 cosec x/sec x+cosec x dx= ∫_0^π/2 3 sec ( π/2 x )+5 cosec ( π/2 x )/sec x+cosec xdx =∫_0^π/2 3 cosec x+5 sec x/s ...

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Byju's Answer

Standard XII

Mathematics

Property 1

∫0π/23 x+5 co...

Question

$\int_{0}^{\frac{π}{2}} \frac{3 s e c x + 5 c o s e c x}{s e c x + c o s e c x} d x =$

π

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2 π

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3 π

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\frac{π}{2}

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Solution

The correct option is B $2 π$
$\int_{0}^{\frac{π}{2}} \frac{3 s e c x + 5 c o s e c x}{s e c x + c o s e c x} d x = \int_{0}^{\frac{π}{2}} \frac{3 s e c (\frac{π}{2} - x) + 5 c o s e c (\frac{π}{2} - x)}{s e c x + c o s e c x} d x$
$= \int_{0}^{\frac{π}{2}} \frac{3 c o s e c x + 5 s e c x}{s e c x + c o s e c x} d x$
$∴ 2 I = \int_{0}^{\frac{π}{2}} \frac{8 s e c x + 8 c o s e c x}{s e c x + c o s e c x} d x = 8 \int_{0}^{\frac{π}{2}} 1 d x = 8 [x]_{0}^{\frac{π}{2}} = 8 \frac{π}{2} = 4 π$

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Similar questions

Q. Evaluate the integral

\int_{0}^{π / 2} \frac{3 sec x + 5 cosec x}{sec x + cosec x} d x

\int_{0}^{\frac{π}{2}} \frac{s e c x}{s e c x + c o s e c x} d x =

Q. If

\frac{π}{2} \int 0 \frac{cot x}{cot x + cosec x} d x = m (π + n),

then

m . n

is equal to :

Q. Find

\int \frac{s e c x}{1 + c o s e c x} d x .

Q. Evaluate :

\int \frac{sec x}{1 + cosec x} d x

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∫π20 3 sec x+5 cosec xsec x+cosec x dx=

The correct option is B 2 π∫π20 3 sec x+5 cosec xsec x+cosec x dx=∫π20 3 sec(π2−x)+5 cosec(π2−x)sec x+cosec xdx =∫π20 3 cosec x+5 sec xsec x+cosec x dx ∴ 2I=∫π20 8 sec x+8 cosec xsec x+cosec x dx=8 ∫π20 1 dx=8[x]π20=8 π2=4π

$\int_{0}^{\frac{π}{2}} \frac{3 s e c x + 5 c o s e c x}{s e c x + c o s e c x} d x =$